GEOSTATISTICAL CHARACTERIZATION OF FRACTAL MODELS OF SURFACES

This article examines fractals with reference to random models of natural surfaces, highlighting the difference between scaling and non-scaling fractal models. It demonstrate that the fractal dimension describes the behaviour near the origin of variograms of the random functions with which a surface is interpreted. The methods for calculating the fractal dimensions based on the Mandelbrot-Richardson graph and the calculation of slopes near the origin of variograms are compared. A brief discussion of the more common techniques for simulating fractals demonstrates their limited usefulness compared to geostatistical techniques. The possibilities of using fractal dimensions and the models and techniques of the fractal approach in general for the study of natural surfaces are then discussed